Decision-Making, Antisaccade Models of

Definition

The antisaccade task in its most typical form (the visually guided antisaccade; Fig. 1) is a reaction time task in which subjects are instructed to perform an immediate eye movement in the opposite direction to a peripheral stimulus, which is presented in their right or left visual field, while they are fixating on a central stimulus (Hallett 1978). Variations of the typical antisaccade (gap antisaccade and overlap antisaccade; Fig. 1) in the horizontal or vertical plane were designed over the years to investigate the effect of the fixation stimulus on the decision to move (Goldring and Fischer 1997; Forbes and Klein 1996; Fischer et al. 1997).

Basic design of the antisaccade task. Typically a participant starts each trial fixating on a stimulus. When a target stimulus appears, the participant must make an eye movement in the opposite direction (antisaccade) of the target stimulus. Visually guided antisaccade: the antisaccade is performed immediately after fixation stimulus (F) is extinguished and target stimulus (T) appears. Gap antisaccade: a gap period exists between disappearance of fixation stimulus and target stimulus appearance. Overlap antisaccade: fixation stimulus remains on during target stimulus presentation

Detailed Description

Basic Antisaccade Behavior

The antisaccade task was first developed to dissociate the stimulus location from the goal of the saccade. During a single trial of the antisaccade task two processes take place: (1) suppression of an erroneous prosaccade toward the peripheral stimulus and (2) generation of a volitional saccade to a position in the opposite direction (antisaccade) (Munoz and Everling 2004). In a single trial, a participant may express any of the following three oculomotor behaviors: (1) the subject makes an antisaccade (an eye movement in the opposite direction of the peripheral stimulus), or (2) the subject makes an erroneous prosaccade (an eye movement in the direction of the peripheral stimulus), or (3) the subject makes an erroneous prosaccade followed by a corrected antisaccade. An error is an eye movement toward the peripheral stimulus instead of the opposite direction. Antisaccade performance involves different metrics such as the mean and standard deviation of the saccade reaction time (SRT) of each eye movement as well as the error rate (Ettinger et al. 2003). Healthy participants typically fail to suppress erroneous prosaccades toward the target on about 20–25% of trials, before correctly saccading toward a location in the opposite direction (Fischer and Weber 1992; Everling and Fischer 1998; Smyrnis et al. 2002; Ettinger et al. 2003; Tatler and Hutton 2007). Unimodal skewed to the right distributions of antisaccades, erroneous prosaccades, and corrected antisaccades are observed. The mean and standard deviation of the antisaccade reaction time from a large cohort of 2006 healthy subjects is reported to be 270 ms and 56 ms, respectively (Evdokimidis et al. 2002). In the same group, the mean and standard deviation of the erroneous prosaccade reaction time is 208 ms and 46 ms, respectively, whereas the mean and standard deviation of the corrected antisaccade reaction time is 146 ms and 85 ms, respectively (Evdokimidis et al. 2002).

Antisaccade Oculomotor Circuit

The antisaccade oculomotor circuit consists of several cortical and subcortical areas including the frontal eye fields (FEF), supplementary eye fields (SEF), dorsolateral prefrontal cortex (DLPFC), anterior cingulate cortex (ACC), lateral intraparietal area (LIP) (parietal eye field (PEF) in the human), basal ganglia, thalamus, superior colliculus (SC), brainstem reticular formation, and cerebellum (Munoz and Everling 2004). Visual information is processed via the retino-geniculo-cortical pathway to primary visual cortex and from there to LIP/PEF and via the retinotectal pathway to the superficial layers of the SC (SCs). LIP is an area in the parietal cortex coding for space. LIP/PEF then projects to both the intermediate layers of the SC (SCi) and frontal cortical oculomotor areas including FEF, SEF, ACC, and DLPFC. FEF is critical for voluntary saccade execution. SEF is implicated in internally guided decision-making and sequencing of saccades. AAC plays a role in conflict resolution and error monitoring. DLPFC is critical in executive function, spatial working memory, and suppressing automated or reflexive responses. These frontal oculomotor areas project to SCi, an area important for decision-making, which then projects to the reticular formation of the brainstem to provide the necessary input to guide saccades.

Another pathway to SCi from the frontal oculomotor areas is through the basal ganglia structures via the direct, indirect, and hyperdirect pathways (Munoz and Everling 2004). Via the direct pathway, frontal areas project to the caudate nucleus (CD), which in turn inhibits the substantia nigra pars reticulata (SNr). SNr disinhibits the SCi and motor nuclei of thalamus, which project back to frontal cortex. Via the indirect pathway, CD projects to the external segment of the globus pallidus (GPe), which in turn projects to the subthalamic nucleus (STN). STN sends excitatory projections to SNr and GPe, which projects via GABAergic connections back to SNr. Via the hyperdirect pathway, cortical regions excite STN, which in turn excite SNr. These complex sets of excitatory and inhibitory projections within the basal ganglia provide a rich set of control mechanisms to help guide voluntary behavior (Coe and Munoz 2017).

Primate Neurophysiology Overview

A number of brain areas in monkeys are involved in the antisaccade task, including the DLPFC (Funahashi et al. 1993), the ACC (Phillips et al. 2010), the LIP (Gottlieb and Goldberg 1999), the SEF (Schlag-Rey et al. 1997; Amador et al. 2004), the FEF (Everling and Munoz 2000), and the SC (Everling et al. 1999). Understanding how neurons in these brain areas participate in the suppression of automatic responses and the generation of antisaccades is crucial for explaining the antisaccade behavior.

Single neuron recordings in FEF and SC have revealed the existence of two distinct and reciprocally activated populations of neurons: the fixation cells and the saccade cells. Fixation cells are tonically active during visual fixation, and their activity ceases when a saccade is executed. On the other hand, saccade cells are silent during fixation but discharge when the animal is making a saccade. In SC, two distinct types of saccade neurons have been recorded: buildup and burst cells (Munoz and Wurtz 1995a, b). A network of inhibitory interneurons is thought to control the reciprocal activation of fixation and saccade neurons (Munoz and Istvan 1998). During fixation in the gap condition (gap prosaccade versus gap antisaccade), fixation activity is greater in the antisaccade trials than in the prosaccade trials in both FEF and SC. This pattern of enhanced fixation activity explains the so-called anti-effect (Munoz and Everling 2004): longer reaction times on antisaccade trials than on prosaccade trials. A few milliseconds into the gap period, there is a drop in activity of fixation neurons and a slow buildup of low-frequency activity of a subset of saccade neurons in both SC (Everling et al. 1999) and FEF (Everling and Munoz 2000). The appearance of the visual stimulus in the right visual field leads to phasic activation of visually responsive saccade neurons in FEF and SC on the contralateral (left) side of the brain, and to phasic inhibition of saccade neurons on the ipsilateral (right) side of the brain. On the prosaccade trials, saccade neurons on the left side discharge a saccadic burst for the rightward prosaccade immediately after the visual phasic response. On antisaccade trials, the saccade neurons in the left FEF and SC are inhibited compared to saccade neurons in the right FEF and SC, which are active to drive the leftward antisaccade.

Recordings from neurons in PFC in rhesus monkeys trained to perform a delayed antisaccade task (Funahashi et al. 1993) revealed that most PFC neurons code the location of the visual stimulus in working memory, and this memory can be engaged to suppress and prescribe a response. Response-coding neurons in smaller percentages were also found, some of which increased their firing rate for the direction of the saccade (e.g., rightward saccade) irrespective of the stimulus location, and others coding for both stimulus location and saccade direction. Similarly, recordings in LIP (Gottlieb and Goldberg 1999) also revealed the majority of LIP neurons reliably coding for the encoded cue location, with only a very small minority encoding for the direction of the upcoming saccade.

Electrical microstimulation in dorsal AAC in monkeys performing alternating blocks of prosaccade and antisaccade trials (Philips et al. 2010) suggested a direct role of AAC in antisaccade performance. On antisaccade trials, microstimulation decreased SRTs for both ipsilateral- and contralateral-directed antisaccades. On the other hand on prosaccade trials, SRTs were increased for saccades contralateral to and decreased for saccades ipsilateral to the stimulated hemisphere.

Finally, recordings from SEF in monkeys (Amador et al. 2004; Schlag-Rey et al. 1997) showed that the vast majority of SEF movement neurons fired significantly more before antisaccades than before prosaccades. The level of their firing was predictive of the correct performance on antisaccades on individual trials.

Antisaccade Performance Across Lifespan

Antisaccade performance varies systematically with age (Munoz et al. 1998; Klein and Foerster 2001; Peltsch et al. 2011). Young children (5–8 years old) have slow SRTs, large intra-subject SRT variance, and the largest error rate in the anti-saccade task. Young adults (20–30 years of age) typically have the fastest SRTs, the lowest intra-subject variance in SRT, and the fewest direction errors. Elderly subjects (60–85 years of age) have slower SRTs than other subject groups. These results demonstrate very strong positive correlation of age and subject antisaccade performance, which may reflect different stages of normal development and degeneration in the nervous system. The dramatic improvement in antisaccade performance observed from the ages of 5 to 15 years is attributed to delayed maturation of the frontal lobes.

Antisaccade performance, on the other hand, of obsessive compulsive (OCD) patients has been variable and contradictory. Initial studies reported increased error rates in OCD patients compared to healthy controls, but no difference in their latencies of antisaccades (Tien et al. 1992). Other studies reported higher antisaccade latencies in OCD patients compared to healthy controls, while their error rate did not differ significantly (Maruff et al. 1999; van der Wee et al. 2006). Another study observed no differences in error rates and latencies of antisaccades between OCD patients and healthy subjects (Kloft et al. 2011). An increase in error rates and in latency of corrected antisaccades was recently reported (Damilou et al. 2016). It is speculated that the OCD antisaccade performance is due to a deficit in erroneous response inhibition control in the oculomotor circuit (Chamberlain et al. 2005; Everling and Fischer 1998; Broerse et al. 2001; Brownstein et al. 2003; Curtis et al. 2001).

Types of Theoretical Models of Antisaccade Performance

Theoretical models of antisaccade performance fall under two categories:

Accumulator models: In these models, the process of decision-making often involves a linear gradual accumulation of information concerning the various potential responses starting at some baseline level S0, which represents the prior expectation, at a constant rate r until it reaches a threshold ST, which represents the confidence level required before the commitment to a particular course of action. Once the decision signal crosses ST, then a response toward the target is initiated. Response time (RT) is measured as the time from the onset of the decision process till when the decision signal crosses ST. Often the rate of accumulation is assumed to vary randomly from trial to trial, with a mean μ and variance σ2 (Reddi and Carpenter 2000). Changes in the baseline level of activity, the rate of accumulation, or the threshold often result in changes in response latency. Prior expectation and level of activation of intention influence the baseline levels of activation.

Neural accumulator models: In these models, the accumulation process is represented by the firing rate of usually a population of neurons. Changes in the rate (slow or fast) of neural firing are usually nonlinear, often competing, and reflect the changes in the rate of accumulation in the linear accumulator.

Below I will review models of various degrees of antisaccade performance from both categories.

Accumulator Models

A notable modeling attempt of the antisaccade paradigm was Noorani’s and Carpenter’s (2013) three-unit model (see Fig. 2a). The model consisted of three LATER units racing to threshold: an ANTI unit, a PRO unit, and a STOP unit. An important model feature was that the ANTI unit was identical (μ and σ) to the PRO unit. In the model, the STOP unit prevented the PRO unit from reaching threshold, thus allowing the ANTI unit to reach a different threshold a little later. The authors hypothesized that the threshold level of the PRO unit was higher than the ANTI unit’s threshold, reflecting the advice given by the experimenters to every subject to avoid errors. How often the STOP unit cancelled the PRO unit depended on its rate of accumulation (μ) and its variance (σ2). The model’s performance was contrasted against the performance of five healthy subjects performing the antisaccade task. The model captured most of the response repertoire observed in the antisaccade task, namely the antisaccades and the erroneous prosaccades, their corresponding latency distributions, and the error response rate. Despite the model’s successes, the model had several shortcomings. The model failed to produce “the erroneous prosaccade followed by the corrected antisaccade” behavior. Moreover, the model postulated the existence of a third inhibitory signal (the STOP signal), which occasionally stopped the erroneous prosaccade response and indirectly allowed just the antisaccade response to be expressed. Recent experimental evidence has challenged the existence of such a third signal (Everling and Johnston 2013).

To address some of these shortcomings, Noorani and Carpenter (2014) extended their previous model (Noorani and Carpenter 2013) by including a RESTART mechanism (see Fig. 2b). In this case, when the PRO unit reached the threshold first, it restarted the ANTI unit allowing it to reach the threshold and generate the antisaccade response. Their new model successfully reproduced the “erroneous prosaccade followed by the corrected antisaccade” behavior, but failed now to reproduce the just erroneous prosaccades. This shortcoming was inherent in their model. The authors postulated that if the STOP signal did not prevent the erroneous prosaccade response, then the PRO unit will always restart the ANTI unit (Noorani and Carpenter 2014). This meant the erroneous prosaccades followed by corrected antisaccades will always be produced. If the STOP unit did prevent the PRO unit, then the ANTI unit would not restart (the corrected antisaccade will not be produced), and an antisaccade response would be generated (Noorani and Carpenter 2014). In either scenario, just an erroneous prosaccade response cannot be generated. The authors claimed in their studies participants never made any just erroneous prosaccades (private communication of the author with Roger Carpenter). However, psychophysical studies of a large group of 2006 participants performing the antisaccade task (Evdokimidis et al. 2002) reported that subjects do make the just erroneous prosaccades, but their response frequency is low. Another limitation of their new model was their consideration that the simulated latency of the corrected antisaccade is the result of the linear sum of latencies of the erroneous prosaccade and the antisaccade minus the latency of the STOP activity. This shortcoming was inherent in the model, because its units are considered linear encoders of the input information.

The three-unit antisaccade model was recently applied to a large sample of Huntington’s disease (HD) patients against healthy controls in an effort to quantitatively predict HD before symptom onset (Wiecki et al. 2016). Experimental RT distributions and error rates of pre-manifest individuals carrying the HD mutation (pre-HD), early symptomatic, and healthy controls performing the antisaccade conflict task were fit using the three-unit antisaccade model. Further machine learning analysis based on fitted model parameters revealed a key executive control parameter was predictive of HD prior to symptom onset, whereas response inhibition processes are impaired only after the motor symptoms are observed.

Extensions of the three-unit antisaccade model were very recently introduced by Aponte et al. (2017) in the form of three probabilistic models, PROSA, SERIA, and SERIAlr. SERIAlr (see Fig. 3) predicted that two decision processes (one early race between a prepotent response toward a target and an endogenously generated signal to cancel this action, and a secondary late race between two units encoding two cue-action mappings) are necessary to properly model the antisaccade task. The two decision processes in SERIAlr were considered to be the sources of early errors, fast erroneous prosaccades in antisaccade trials, and late errors, late actions incongruent with the cue presented. Bayesian model comparison showed that the SERIAlr model explains the data better than other competing models that did not incorporate a late decision process. Early decision processes were predicted to be insensitive to cue presented in every trial. Changes in reaction time and error rate due to probability of trial type were best explained by faster or slower inhibition in the model.

SERIAlr model. The presentation of a visual cue (target) triggers the race of four independent units.. The Stop unit can stop an early response. The late decision process is triggered by the competition between two further units

Neural Accumulator Models

Rate-Based Models

The first ever attempt to simulate the antisaccade task and uncover its neural mechanisms was made by Cutsuridis et al. (2007a) when they introduced a neural nonlinear accumulator model with competition via lateral inhibition between its components. The model was a 1D layer neuronal arrangement of the intermediate layer of SC with three different types of cells, namely the fixation, buildup, and burst neurons (Trappenberg et al. 2001) (see Fig. 4). In the model, the fixation cells were activated by the fixation stimulus, and the buildup and burst cells by two inputs, a reactive input that represented the erroneous prosaccade motor plan and originated from the lateral intraparietal (LIP) area (Gottlieb and Goldberg 1999) and a planned input which represented the antisaccade motor plan and originated from FEF (Everling and Munoz 2000). The inputs were linear ramping processes till a maximum value after which they were either abruptly brought or smoothly decayed to zero. The slopes values of these linearly ramping processes took values from Gaussian distributions with different means and standard deviations for each input. Both inputs were integrated by spatially distant buildup and burst cells, which competed one another via lateral inhibition (Munoz and Istvan 1998). Each simulation trial started with the model fixation cells firing maximally for as much time as the subjects were fixating to the central stimulus and buildup and burst cells being silent. As soon as the peripheral stimulus appeared and the subjects had to make an antisaccade, then the model fixation activity started to decay to zero and the builup cell activity stated to rise. In the model, the buildup cells had the role of accumulator cells that integrated evidence till some user pre-set threshold. Once the threshold was crossed, then the cue was given to the model burst cells to fire maximally, but for a short period of time (phasic activation). In the model, the burst activity represented the final motor command given to the eyes to move. Occasionally, in some simulated trials both erroneous prosaccade and antisaccade buildup cells crossed the threshold, which then cued their corresponding burst cells to fire. Behaviorally that meant that the virtual subject made an erroneous prosaccade first and corrected with an antisaccade. The model was able to produce all three oculomotor behaviors of the antisaccade task, namely the erroneous prosaccade, the antisaccade, and the corrected antisaccade. The model was also able to simulate accurately the antisaccade performance (latency distributions of the erroneous prosaccades and antisaccades as well as the error rates) of 10 virtual groups of participants with only five free parameters. The model predicted that competition via lateral inhibition and not a third inhibitory signal accounts for the antisaccade performance of a large cohort of healthy participants. Despite its successes the model suffered from shortcomings. The simulated discharged rates of the fixation and buildup cells were unrealistically high (roughly 600 Hz) (Munoz and Wurz 1993, 1995a, b). For lower discharged rates the model can still accurately simulate the behavioral and neurophysiological properties of the antisaccade task, but for different parameter values (unpublished observations). Furthermore, the model failed to uncover the ionic and synaptic mechanisms that may produce the range of values of input slopes needed to produce the latency distributions of the erroneous prosaccades and antisaccades.

Recently, Cutsuridis extended his neural nonlinear accumulator with competition model of antisaccade performance (Cutsuridis et al. 2007a) into the disorder domains of schizophrenia and obsessive-compulsive disorder (OCD) (Cutsuridis et al. 2014; Cutsuridis 2017a, b). In the new model (see Fig. 5), variations in the integration constants of buildup cell activities in the model SC and not in the slopes of the ramping phases of the cortical inputs produced the error rates and latency distributions of the erroneous prosaccades, antisaccades, and corrected antisaccades of healthy controls (Ettinger et al. 2003), schizophrenia, and OCD (Damilou et al. 2016) suffering subjects. The model showed that the poor antisaccade performance in schizophrenia is due to a more noisy accumulation of information, but the schizophrenia patients are as confident (threshold level is unchanged) as their healthy counterparts (Cutsuridis et al. 2014). In contrast, in OCD, the accumulation of information is also noisy, but the OCD subjects are less confident (threshold level is changed) than the healthy participants (Cutsuridis 2017b). In both disorders, the model predicted the antisaccade performance is not due to a deficit in the top-down inhibitory control of the erroneous response as many speculated, but instead it is due to a local inhibitory mechanism in the form of a competitive race to a threshold between the buildup cell representations of the erroneous prosaccade and antisaccade in SC. In favor of this competitive race to a threshold between competing prosaccade and antisaccade signals is the Massen (2004) study, which selectively manipulated the exogenous and endogenous processes in the antisaccade task (e.g., slowing down or speeding up one of these or both processes) and observed the effects of this manipulation on error rate. Massen (2004) observed that if a manipulation slowed the generation of antisaccades, while having no effect on prosaccade generation, then the error rate was increased. If, however, manipulation influenced both pro- and antisaccade generation to the same degree, then the error rate remained unchanged. Massen (2004) argued that antisaccade performance is explained in terms of a competition between two parallel programs for saccade execution: if the volitional antisaccade is programmed fast enough (e.g., reaches some threshold for activation), then it will win the competition, and the reflexive prosaccade will be cancelled. Alternatively, if the prosaccade is programmed fast enough or the computation for the antisaccade is too slow), an erroneous prosaccade will be made first followed by the correct antisaccade. This account in line with Cutsuridis et al.’s (2007a, 2014, 2017b) computational studies favored the concept of an active inhibitory mechanism in the form of competition between competing decision signals as being critical to antisaccade performance.

Spiking Neuron Models

To uncover the ionic and synaptic mechanisms that produced the range of values of accumulation rates needed to produce the latency distributions of the erroneous prosaccades and antisaccades in Cutsuridis et al.’s (2007a) model, the same group (Cutsuridis et al. 2007b) introduced a multi-modular neural network model consisting of two cortical modules (FEF and LIP) that drove the SC module to decide the winning motor command to move the eyes (Fig. 4). Each cortical module was a network of Hodgkin-Huxley type excitatory and inhibitory neurons connected together. The SC module was the same as in Cutsuridis et al.’s (2007a) study. No connectivity was assumed between the cortical modules, although it has been experimentally observed (Schall 1997). Symmetric and asymmetric connection types were tried. Background noise and synaptic noise were also included in the cortical model neurons and in their connections to simulate homogeneous and heterogeneous neuronal firings. The population activity from each cortical network was extracted and a line was fitted to its ramping activity to estimate its slope. Variations in all model ionic and synaptic conductances were attempted to uncover which current(s) and what range of their conductance values reproduced the full range of slope values of the planned and reactive inputs to the SC model needed to reproduce the latency distributions and error rates of the virtual groups of participants in the Cutsuridis et al.’s (2007a) study. The model predicted that only conductance variations of the persistent Na+, NMDA and AMPA currents could produce the necessary slope variability in the cortical decision signals to reproduce the latency distributions and response probabilities of the virtual subjects.

Recently, a two-module spiking with competition network model of antisaccade performance was advanced by Lo and Wang (2016). The model consisting of sensorimotor remapping and action selection modules, the latter endowed by a “Stop” process through tonic inhibition, both under the modulation of rule-dependent control revealed the circuit mechanisms for the experimentally observed distributions of erroneous responses in the antisaccade task. In the model, fast errors resulted from failing to inhibit the quick automatic responses and therefore exhibited very short response times. Slow errors, on the other hand, were due to an incorrect decision in the remapping process and exhibited long response times comparable to those of correct antisaccade responses.